Study of new analyzing method of LDPC codes and there practical encoding algorithm based on mathematical techniques on the system of linear equations

• Project/Area Number: 24560477
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Communication/Network engineering
• Research Institution: Sophia University
• Principal Investigator: SHIBUYA Tomoharu 上智大学, 理工学部, 准教授 (20262280)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: ＬＤＰＣ符号 / 誤り訂正符号 / 符号化 / 線形連立方程式 / ＤＭ分解 / ヤコビ法 / LDPC符号 / 復号 / 復号法 / 符号化法 / 線形符号 / 線形符号の符号化法 / 復号性能の解析

Outline of Final Research Achievements

In this research, we have proposed a fast encoding algorithm for LDPC codes and developed a method to evaluate their performance. More concretely, we carefully studied the characteristics of DM decomposition and Jacobi method, both of which can be utilized to efficiently solve systems of linear equations, and then succeeded (1) to propose a new encoding algorithm that can be applied to arbitrary linear codes, and (2) to compare error performance of SC-LDPC codes, that are recently invented, with that of conventional LDPC codes.

Research Products

• [Journal Article] Efficient Linear Time Encoding for LDPC Codes (2014)
  • Author(s): T. Shibuya and K.Kobayashi
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E97.A Issue: 7 Pages: 1556-1567
  • DOI: 10.1587/transfun.E97.A.1556
  • NAID: 130004519183
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Single Error Correcting Quantum Codes for the Amplitude Damping Channel Based on Classical Codes over <i>GF</i>(7) (2014)
  • Author(s): K. Kodaira, M. Wada, and T. Shibuya
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E97.A Issue: 11 Pages: 2247-2253
  • DOI: 10.1587/transfun.E97.A.2247
  • NAID: 130004706377
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Efficient Linear Time Encoding for LDPC Codes (2014)
  • Author(s): T. Shibuya and K. Kobayashi
  • Journal Title: IEICE Trans. Fundmentals Volume: E97-A
  • NAID: 130004519183
  • Peer Reviewed
• [Journal Article] On the Dependence of Error Performance of Spatially Coupled LDPC Codes on Their Design Parameters (2013)
  • Author(s): H. Ihara and T. Shibuya
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E96.A Issue: 12 Pages: 2447-2451
  • DOI: 10.1587/transfun.E96.A.2447
  • NAID: 130003385295
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed
• [Journal Article] On the dependence of error performance of spatially coupled LDPC codes on their design parameters (2013)
  • Author(s): Hiroyuki Ihara, Tomoharu Shibuya
  • Journal Title: IEICE Trans. on Fundamentals Volume: E96-A
  • NAID: 130003385295
  • Peer Reviewed
• [Presentation] On the Condition on Classical Codes to Construct Quantum Error Correcting Codes for Amplitude Damping Channel (2014)
  • Author(s): K. Kodaira and T. Shibuya
  • Organizer: ISITA2014
  • Place of Presentation: Melbourne Convention & Exhibition Center (Australia)
  • Year and Date: 2014-10-26 – 2014-10-29
• [Presentation] Entanglement-Assisted Quantum Error-Correcting Codes Based on the Circulant Permutation Matrix (2014)
  • Author(s): M. Wada, K. Kodaira, and T. Shibuya
  • Organizer: ISITA2014
  • Place of Presentation: Melbourne Convention & Exhibition Center (Australia)
  • Year and Date: 2014-10-26 – 2014-10-29
• [Presentation] Classical Codes over GF(q) for Mersenne Prime q and Their Application to Quantum Codes for the AD Channel (2013)
  • Author(s): K. Kodaira and T. Shibuya
  • Organizer: 第36回情報理論とその応用シンポジウム
  • Place of Presentation: 静岡県伊東市
• [Presentation] Compressed Encodingを利用したRank Modulationにおける極小支配集合とその構成 (2013)
  • Author(s): 神林雄也, 渋谷智治
  • Organizer: 電子情報通信学会情報理論研究会
  • Place of Presentation: 関西学院大学大阪梅田キャンパス
• [Presentation] On the dependence of error performance of spatially coupled LDPC codes on their design parameters (2012)
  • Author(s): Hiroyuki Ihara, Tomoharu Shibuya
  • Organizer: 電子情報通信学会情報理論研究会
  • Place of Presentation: 豊田工業大学
• [Presentation] 代数的符号理論 (2012)
  • Author(s): 渋谷智治
  • Organizer: 誤り訂正符号のワークショップ
  • Place of Presentation: 草津セミナーハウス
  • Invited
• [Presentation] Generalization of Lu's Linear Time Encoding Algorithm for LDPC Codes (2012)
  • Author(s): Kazuki Kobayashi, Tomoharu Shibuya
  • Organizer: 2012 International Symposium on Information Theory and its Applications
  • Place of Presentation: Hawaii, USA